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India is one of the worst hit regions by the second wave of COVID-19 pandemic and ‘Black fungus’ epidemic. This paper revisits the Bombay Plague epidemic of India and presents six fractional-order models (FOMs) of the epidemic based on observational data. The models reveal chaotic dispersion and interactive coupling between multiple species of rodents. Suitable controllers based on fuzzy logic concept are designed to stabilise chaos to an infection-free equilibrium as well as to synchronise a chaotic trajectory with a regular non-chaotic one so that the unpredictability dies out. An FOM of COVID-19 is also proposed that displays chaotic propagation similar to the plague models. The index of memory and heredity that characterise FOMs are found to be crucial parameters in understanding the progression of the epidemics, capture the behaviour of transmission more accurately and reveal enriched complex dynamics of periodic to chaotic evolution, which otherwise remain unobserved in the integral models. The theoretical analyses successfully validated by numerical simulations signify that the results of the past Plague epidemic can be a pathway to identify infected regions with the closest scenarios for the present second wave of Covid-19, forecast the course of the outbreak, and adopt necessary control measures to eliminate chaotic transmission of the pandemic.

The operation of memristive, meminductive and memcapacitive circuit components depend on their history of devices, i.e. they are memory dependent. This paper proposes new fractional-order (FO) models of four such circuits since FO derivative is calculated using the past history of time and helps in understanding the memory-dependent dynamics of these memory devices better as compared to the integral derivative. Interestingly, these fractional-order memristive, meminductive and memcapacitive systems (FOMMMSs) display a myriad of dynamics such as ranging from coexisting to hidden attractors, chaotic to hyperchaotic attractors, periodic orbits to stable foci, bursting oscillations transitioning from chaos to periodic states and vice versa, offset boosting phenomenon, and a varied nature of infinite equilibria. The proposed fractional-order systems can have a number of applications such as in oscillator circuits, and secure communication due to the increased randomness of hidden multistability. The theoretical analyses of existence of multistability and hidden attractors in the proposed FOMMMSs comply with that of the numerical simulation and circuit implementation results.

Chaotic systems with either a self-excited attractor or a hidden attractor are prevalent in the research paradigm. But a composite attractor of a chaotic system that exhibits both self-excited attractors and hidden attractors with time is rare. Compounding of a chaotic system is devised to enhance the richness of the system as it exhibits different behaviors with time. This paper presents a two-stage technique for generating a compound-chaotic system by combining eight subsystems from Chameleon chaotic system. The first stage is the design of a nonautonomous piecewise function. The second stage is to generate a compound system using the designed function. The compound system exhibits a composite attractor that is a mix of self-excited and hidden attractors with time. The composite attractor is generated with the variation of the equilibrium points in the eight subsystems due to the designed function. The resultant attractor of the compound-chaotic system is termed as a composite attractor since it has both the self-excited and hidden attractors. Transient chaos and coexistence of attractors are also observed in the system. The proposed compound-chaotic system is analyzed using the available tools and the paper’s claims are validated.

The basic parameters of an electromagnetic levitation systems are resistance of the coil, inductance of the coil, air-gap between magnet and the object, coil current, mass of the object, controller parameters and so on. The levitation systems are highly unstable and strongly non-linear. In real-life applications, these parameters are supposed to vary. A proportional–integral controller for the inner current control loop and a lead compensator for the position control loop have been designed and tested. The performance study under various parametric effects has been investigated broadly. Finally, both the stability for the proposed levitation system has been achieved with a better operating zone using linear state variable feedback controllers. The system dynamic performances have been recorded for variations of physical system parameters. The sensitivity/robustness of the set-up has been studied. This study will give an insight for designing any corrective measures and an overall idea to develop a levitation system.

This paper deals with (i) damping improvement and (ii) energy management of a DC microgrid for improvement of its stability. The direct current (DC) microgrid has a solar-photovoltaic system as a renewable source and fuel cell-battery combination as a backup system to supply power to constant power loads (CPLs). The presence of CPLs in a DC microgrid makes the stability problem more challenging since the negative impedance characteristics of CPLs bring instability into the system. A control approach using interconnection and damping assignment-passivity based control (IDA-PBC) is proposed in this paper to address both the objectives. The proposed control approach provides an efficient energy management, the required damping and also maintains the stability by making the system passive. The tuning parameters of the control laws are adapted incorporating the state of charge (SoC) for the effective energy management. In addition, an integral action is added with the proposed control laws to eliminate the steady-state error in the voltage level of the DC bus and load bus. The proposed IDA-PBC control along with an integral action is compared with four other control approaches, and reveals its better performances. The MATLAB/Simulink results show that the proposed control technique provides better responses in terms of providing damping and effective energy management.

A projective synchronisation strategy is designed in this paper to synchronise a master manipulator having 12 states modelled using the assumed modes method and the slave manipulator with 8 states ...

In this paper, a hierarchical virtual inertia control technique for a bidirectional DC–DC converter is proposed to enhance inertia of an isolated DC microgrid through the DC bus voltage regulation....

In this study, energy management and damping improvement of a DC microgrid are proposed by using an interconnection and damping assignment–passivity-based control (IDA–PBC) technique. The control technique is applied for (i) the grid connected inverter and (ii) the DC–DC converters connected with fuel cell and battery of the DC microgrid to control the DC bus voltage. The IDA–PBC generates the control laws with the desired energy function for the current controller of the converters based on the generation from the renewable power generators and load demand. In addition, an integral action is added with the IDA–PBC control laws to reduce the steady-state error in the DC bus voltage. The parameters of the IDA–PBC technique are tuned based on the state of charge of the battery and grid availability for a smooth transition between the operating modes and better energy management. It is proved that the derived energy function satisfies the Lyapunov stability criterion. Simulations are carried out in MATLAB/Simulink to test the performance of the proposed control technique. The results show that the proposed technique provides the desired damping and energy management.

This paper focuses on the comparative performances between a Sliding Mode Controller (SMC) and a Fractional-Order SMC (FOSMC). Both the SMC and FOSMC are applied to position control of a ferromagnetic ball against gravity in a Magnetic Levitation (MagLev) system. This paper is the extended version of Roy et al. (in: 2017 Indian control conference (ICC), pp 473–478, 2017). In addition to the contribution of Roy et al. (2017), this paper (i) shows the better potential of an FOSMC over a SMC which is illustrated analytically and (ii) finds the bounds of uncertainty of the parameters of the MagLev system using frequency domain analysis. Experimental results validate the theoretical propositions. The comparative analysis based on these results reveals that the FOSMC performs better than the SMC in terms of tracking accuracy, speed of response, chattering, control effort, and control energy.

In this paper, a three-dimensional novel chaotic system and its projective synchronisation are investigated. The proposed chaotic system has no equilibria. The topological structure of proposed chaotic system is different form Lorenz, Rossler and Chen systems. Different qualitative and quantitative tools such as time series, phase plane, Poincare section, bifurcation plot, Lyapunov exponents, Lyapunov spectrum, and Lyapunov dimension are used to evidence the chaotic behaviour of the proposed system. Further, the projective synchronisation between the proposed chaotic systems is achieved using nonlinear active control. Active control laws are designed, by using sum of the relevant variables of the proposed chaotic systems, to ensure the convergence of error dynamics. The required global asymptotic stability condition is derived using Lyapunov stability theory. Simulation is done in MATLAB environment to verify the theoretical approach. Simulation results reveal that the objectives of the paper are achieved successfully.

This paper puts forward the inter network synchronisation of complex dynamical networks (CDNs) using drive-response philosophy. The inter networks consist of a drive network (each node represents a hyperchaotic system) and a response network (consists of chaotic system at each node). Synchronisation is achieved using a novel proportional integral (PI) based sliding mode control (SMC) scheme and inter network synchronisation criterion is derived. Unlike the conventional SMC technique, the proposed proportional integral-sliding mode control (PI-SMC) technique does not result decoupled error dynamics. A smooth switching surface is designed to eliminate the chattering effect. The different network configurations: small-world and scale-free networks, are simulated and the simulation results show that the proposed synchronisation scheme is effective for the inter network synchronisation between two or more CDNs. The effect of relevant parameters on the synchronisation process in the Watts-Strogatz (WS) small-world and Barabasi-Albert (BA) scale-free networks are analysed. Finally, the proposed PI-SMC technique is compared with standard SMC technique to justify the advantages over the standard SMC technique.

A 3-D multi-state-time-delayed chaotic system consisting of a externally added memristive element is proposed in this research work. The proposed system belongs to the family of hidden attractor and displaying multi-scroll behaviours. Multi-state-time-delayed chaotic system with multi-scroll is not seen in the literature. The chaotic behaviour of the proposed time-delayed chaotic system is investigated thoroughly by bifurcation analysis, phase-plane analysis, and instantaneous phase plot. Finally, a sliding mode controller is proposed for switching synchronisation between the two identical proposed multi-state-time-delayed chaotic systems including externally added memristor with disturbances.The simulation results confirm the claim of the paper.

This paper presents a novel simple 4-D dissipative autonomous hyperchaotic system with a saddle-point index-2 equilibrium point. The dynamics of the new system consists of nine terms with two nonlinear terms. Thus, the proposed system is one of the simplest 4-D hyperchaotic systems. The new system also shows multistability behavior for some range of its parameters. Bifurcation diagrams, Lyapunov spectrum, Kaplan-Yorke dimension, and phase plots are used to analyze the complex dynamical behavior of the system. The discrete-time equivalent of the presented hyperchaotic system is made by using the Euler algorithm for improving the embedded chaos-based engineering applications on FPGA. Then, the design of a novel TRNG having chaotic entropy seed has been performed utilizing FPGA-based 4-D hyperchaotic system structure. The Euler-based model in the creation phase on FPGA has been described using VHDL with 32-bit IEEE 754-1985 floating-point format. The designed hyperchaotic system and TRNG unit have been synthesized using Xilinx ISE Design Tools, and chip statistics obtained from place-and-route process have been presented by testing in the Virtex-6 FPGA chip of Xilinx family. The numbers generated in high data rates of 185.447 Mbit/s have been obtained with 370.894 MHz clock frequency for the implementation of the novel TRNG unit. In the last stage, randomness tests of the generated random numbers have been carried out and the generated random numbers have passed successfully all randomness tests.

The paper reports a modified 4D autonomous hyperchaotic system with an unusual characteristic. The modified system exhibits dissipative behavior for some ranges of a parameter and conservative behavior for the other ranges of the same parameter. Thus, there is a switching between dissipative and conservative behaviors of the proposed system. In the conservative range, the system exhibits chaotic orbit. Again in the dissipative range, the system, with its considered sets of parameters, exhibits strange attractors. Thus, both the dissipative and conservative behaviors exist in the same system with the switching of its parameter. Such behavior of a system is rarely reported in the literature. Further, the equilibria of the system are located on the surface-shape. The proposed system is implemented and simulated using Field Programmable Gate Array (FPGA) and Multisim simulation softwares.